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The single-index model (SIM) is a simple asset pricing model to measure both the risk and the return of a stock. The model has been developed by William Sharpe in 1963 and is commonly used in the finance industry. Mathematically the SIM is expressed as: where:

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  • Single-index model
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  • Das Single-Index-Modell (kurz: SIM, auch Ein-Index-Modell) ist eine Theorie der optimalen Portfolioauswahl.Ziel des Single-Index-Modells ist die Vereinfachung hin zu nur einem Einflussfaktor. Damit soll ein strukturelles Gebilde geschaffen werden, das die Renditen rein statistisch erklärt. Es handelt sich um eine Art Regressionszusammenhang. Im SIM müssen weniger Parameter als im vollen Markowitz-Modell geschätzt werden.
  • The single-index model (SIM) is a simple asset pricing model to measure both the risk and the return of a stock. The model has been developed by William Sharpe in 1963 and is commonly used in the finance industry. Mathematically the SIM is expressed as: where:
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  • Das Single-Index-Modell (kurz: SIM, auch Ein-Index-Modell) ist eine Theorie der optimalen Portfolioauswahl.Ziel des Single-Index-Modells ist die Vereinfachung hin zu nur einem Einflussfaktor. Damit soll ein strukturelles Gebilde geschaffen werden, das die Renditen rein statistisch erklärt. Es handelt sich um eine Art Regressionszusammenhang. Im SIM müssen weniger Parameter als im vollen Markowitz-Modell geschätzt werden.
  • The single-index model (SIM) is a simple asset pricing model to measure both the risk and the return of a stock. The model has been developed by William Sharpe in 1963 and is commonly used in the finance industry. Mathematically the SIM is expressed as: where: rit is return to stock i in period trf is the risk free rate (i.e. the interest rate on treasury bills)rmt is the return to the market portfolio in period t is the stock's alpha, or abnormal return is the stock's beta, or responsiveness to the market returnNote that is called the excess return on the stock, the excess return on the market are the residual (random) returns, which are assumed independent normally distributed with mean zero and standard deviation These equations show that the stock return is influenced by the market (beta), has a firm specific expected value (alpha) and firm-specific unexpected component (residual). Each stock's performance is in relation to the performance of a market index (such as the All Ordinaries). Security analysts often use the SIM for such functions as computing stock betas, evaluating stock selection skills, and conducting event studies.
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